Faults (or failures) are unavoidable in complex systems such as supply chains, power grids, and healthcare systems. Faults have major cost implications and can cause catastrophic events. For instance, the annual cost of power interruptions in the U.S. is estimated between $22 and $135 billion. See LaCommare, K. H. and Eto, J. H., 2004, Understanding the Cost of Power Interruptions to U.S. Electricity Consumers, Energy Analysis Department, Ernest Orlando Lawrence Berkeley National Laboratory, University of California Berkeley, Berkeley, Calif. 94720. A healthcare insurance company covering 10 million members is estimated to pay $400 million a year in overpayments due to unintentional (mistakes made by patients, providers, and insurance companies) and intentional errors (fraudulent claims). See Anand, A., 2008, “A data mining framework for identifying claim overpayments for the health insurance industry,” in Proc. of the 3rd INFORMS Workshop on Data Mining and Health Informatics. 
Most faults in a system are caused by a few faulty sources which require repair. These faulty sources can cause other downstream faults to subsystems that are dependent upon the faulty sources. Accordingly, these downstream faults are repaired once the faulty sources are repaired. For instance, products flow from supplier A downstream to customer B in a supply chain. A fault occurs if B does not receive certain products by a predetermined time. The fault at B, however, often is caused by faults at A or faults at other manufacturing or distribution entities along the path from A to B. The fault at B, therefore, is repaired after any fault at A and the other faulty entities are repaired. Similarly, a fault occurs in an electrical power grid if a bus (transmission path) cannot provide electricity to a customer. If the bus itself is damaged, and has, consequently, caused damage to downstream electrical components, the bus is repaired before repairing the damaged downstream electrical components.
Although the issue of how to prevent and repair failures (or faults) with an optimal sequence is an important issue in the art, it, conventionally, has largely been left open. See Ang, C. C., 2006, Optimized Recovery of Damaged Electrical Power Grids, M. S. Thesis, Naval Postgraduate School, Monterey, Calif., USA. Accordingly, a need in the art exists for techniques to generate improved failure (or fault) prevention and repair (“FPR”) sequences.